On the stochastic nonlinear Schrödinger equation in dimension 2

Abstract : We consider a non linear Schrödinger equation on a compact manifold of dimension d subject to some multiplicative random perturbation. Using some stochastic Strichartz inequality, we prove the existence and uniqueness of a maximal solution in H1 under some general conditions on the diffusion coefficient. Under stronger conditions on the noise, the nonlinearity and the diffusion coefficient, we deduce the existence of a global solution when d = 2. This is a joint work with Z. Brzezniak.
Type de document :
Communication dans un congrès
Women in Applied Mathematics, May 2011, Heraklion, Greece. http://www.acmac.uoc.gr/WAM2011/program.html, 2011
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https://hal.archives-ouvertes.fr/hal-00624578
Contributeur : Annie Millet <>
Soumis le : lundi 19 septembre 2011 - 11:10:20
Dernière modification le : dimanche 12 novembre 2017 - 01:08:41

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  • HAL Id : hal-00624578, version 1

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Annie Millet, Zdzislaw Brzezniak. On the stochastic nonlinear Schrödinger equation in dimension 2. Women in Applied Mathematics, May 2011, Heraklion, Greece. http://www.acmac.uoc.gr/WAM2011/program.html, 2011. 〈hal-00624578〉

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